Course detail

Mathematical Modelling

FSI-PMMAcad. year: 2017/2018

Due to the development of computer technology, the numerical simulation has become helpful in designing and optimising foundry processes. Mathematical simulation is aimed at the tuning of the designed technology in the phase of production preparation in order to avoid expensive experimental testing. The simulation of foundry processes connects numerical methods, physics and computer technology. It enables the study of processes during melt flow, solidification and cooling of castings.

Learning outcomes of the course unit

Student will acquire the knowledge of 3D modelling of castings, definition of initial and boundary conditions of numerical simulation, evaluation of simulation results. The optimisation of gating and feeding systems is done using real castings and is performed for all foundry processes (gravity sand and die casting, high pressure die casting, investment casting, semi-solid processes). Calculation of production costs and sale price of castings together with Pacyna’s classification of castings is described. Relationships between other modules for thermo-mechanical calculation of castings are shown. The calculations are carried out with the support of modern software products.


Basic knowledge of Foundry technology, knowledge of liquid flows and heat transfer, basic computer skills


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

BONOLLO, F., ODORIZZI, S. Numerical Simulation of Foundry Processes. 1st ed. Padova: S.G.E., 2001, 264 p. ISBN 88-86281-63-3
Herman, A. a kol.: Počítačové simulace ve slévárenství, Vydavatelství ČVUT, 2000
Nová, I.:Tepelné procesy ve slévárenských formách, TU Liberec, 2003 (CS)

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

Course – unit credit requirements-optimisation of real casting technology, participation in the lessons
Exam - written and oral parts

Language of instruction


Work placements

Not applicable.


The aim of the course is to explain all the stages of simulation preparation and to give a compact view of the possibilities of computer assisted systems in the area of foundry processes.

Specification of controlled education, way of implementation and compensation for absences

Participation in seminars is required. An apologized absence from seminars may be compensated by individual work.

Classification of course in study plans

  • Programme M2I-P Master's

    branch M-SLE , 1. year of study, summer semester, 4 credits, compulsory
    branch M-SLE , 1. year of study, summer semester, 4 credits, compulsory

Type of course unit



13 hours, optionally

Teacher / Lecturer


1. Introduction to numerical simulation of foundry processes
2. Application of CAD system in foundry processes
3. Methods of numerical simulation
4. Basic knowledge of heat transfer
5. Initial condition definition
6. Boundary condition definition
7. Thermo-physical properties
8. Calculation of porosity defects in casting
9. Simulation of gravity sand casting technology
10. Simulation of high-pressure die casting technology
11. Investment casting technology
12. Special processes – semi-solid processes
13. Post-processing and industrial cases

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer


1. Geometry design – data import and export
2. Preparation of surface and volume meshes
3. Repairing of bad meshes
4. Definition of initial and boundary conditions
5. Calculation definition – modules, calculation steps
6. Examples of gravity casting calculation
7. Examples of pressure casting calculation
8. Examples of investment casting calculation
9. Calculation of special processes
10. Porosity calculation
11. Optimisation of gating and feeding systems
12. Post-processing
13. Results validation